Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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BD, ęquidiſtante, & </
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<
s
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">quia latus, AB, indefinitè productum oc-
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currit baſi, etiam dictum baſi ęquidiſtans planum occurret indefini-
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tè productum ipſi baſi, quod eſt abſurdum, non igitur planum du-
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ctum per, A, baſi, BD, ęquidiſtans conicum tangit vel ſecat in a-
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lio, quam in puncto, A, ergo, A, erit illius vnicus vertex reſpectu
<
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baſis, BD, quod erat oſtendendum.</
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<
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<
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">_C_Vm autem dicemus verticem alicuius conici, intelligemus ſemper
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ipſum reſpectu baſis aſſumptum, ideſt punctum, curin reuolutie-
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ne innititur latus cylindrict, niſi aliud explicetur.</
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<
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">THEOREMA XIII. PROPOS. XVI.</
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">SI conicus ſecetur vtcumque per verticem ducto plano,
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concepta in ipſo ſigura, vel figuræ, erit triangulus, vel
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trianguli.</
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<
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<
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">Secetur quilibet conicus, ABF, plano vtcumque per verticem
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ducto, quod in eo producat figuram, ſiue figuras, ABC, AEF.
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0052-01
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Dico eas eſſe triangulos, Sit com-
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munis ſectio illius, & </
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">baſis pro-
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ducti plani, tota, BF, cuius, CE,
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portio maneat extra baſim, eſt igi-
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tur, BF, recta linea, dico etiam
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eſſe rectas ipſas, AB, AC, AE,
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AF, ſienim non eſt, AB, recta,
<
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ducatur in plano figurę, ABC, re-
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cta, AOB, igitur, AOB, quę
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iungit punctum, B, & </
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<
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">verticem coni eſt latus conici, ABF, ergo
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eſt in ſuperficie coniculari, & </
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<
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">eſt etiam in plano figurę, ABC, ergo
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eſt in eorum communi ſectione, ideſt cadit ſuper, AB, igitur, AB,
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erit recta linea, eodem modo oſtendemus ipſas, AC, AE, AF, eſſe
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rectas, & </
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<
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xml:space
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">ideò erit, ABC, triangulus, vt etiam, AEF, quod erat
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oſtendendum.</
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">_E_Odem modo nobis innoteſcit figuras, quæ extra conicum fiunt eſſe
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triangulos, ideſt, ACE, eſſe triangulum, & </
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<
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gratur, ſcilicet, ABF, pariter eſſe triangulum.</
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